A cross-correlation method for measuring line formation heights in the solar photosphere

Abstract

Context. Detailed 3D-simulations of magneto-convection in the solar photosphere are now available. They intend to capture the main physical mechanisms at play in this boundary layer, where complex physical phenomena, such as convective overshooting and small scale magnetic dynamo take place. But numerical limitations in spatial resolution and in box-size are likely to affect the description of some relevant physical scales, so simulations need to be compared to independent observations allowing us to explore the full height range of the photosphere.
Aims: Here we focus on a model-independent method for measuring line formation depths. We construct images of the photosphere at constant continuum opacity levels from the low to the upper photosphere and we show how they can be used to measure systematic displacements of granular structures with height. The method is applied to determine the formation height of the 630 nm Fe i line pair. We compare our measurements to the results of 3D simulations.
Methods: We analyze high resolution spectroscopic scans obtained in the 630 nm Fe i line pair at varying heliocentric angles along the north-south polar axis of the Sun, with SOT onboard Hinode. We implement a new strategy for correcting the images observed at different line cords from spurious Doppler effects. The cross-correlations between continuum images and line core images show a clear anti-correlation peak due to the contrast inversion of the granulation in the upper photosphere, as predicted by magnetohydrodynamic (MHD) simulations.
Results: The anti-correlation peak is shifted by the perspective effect and by horizontal velocity effects. Both effects may be distinguished because they have different center-to-limb variations. The measurement of the perspective shift allows us to determine the line core formation heights and their center-to-limb variations. The results are in good agreement with 3D- MHD simulations for images close to disk center, but close to the solar limb we measure larger formation heights than what is predicted by the simulations, which seem to fail in modeling properly the upper layers of the photosphere. As the granulation contrast inversion is observed at line centers, we can safely conclude that the height of the contrast inversion layer is smaller than 200 km.